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1 N5FOR OFFICIAL USE X844/75/01 National Quali cations 018 Mark Applications of Mathematics Paper 1 (Non-Calculator) THURSDAY, 3 MAY 9:00 AM 10:05 AM *X * Fill in these boxes and read what is printed below. Full name of centre Town Forename(s) Surname Number of seat Date of birth Day Month Year Scottish candidate number Total marks 45 Attempt ALL questions. You may NOT use a calculator. To earn full marks you must show your working in your answers. State the units for your answer where appropriate. Write your answers clearly in the spaces provided in this booklet. Additional space for answers is provided at the end of this booklet. If you use this space you must clearly identify the question number you are attempting. Use blue or black ink. Before leaving the examination room you must give this booklet to the Invigilator; if you do not, you may lose all the marks for this paper. *X * A/HTP

2 FORMULAE LIST Circumference of a circle: C = πd Area of a circle: A= πr Theorem of Pythagoras: c b a + b = c a Volume of a cylinder: V= πrh Volume of a prism: V = Ah Volume of a cone: V= 1 πrh 3 Volume of a sphere: V = 4 π 3 3 r Standard deviation: Σ( x x) Σ x (Σ x) n s = =, where n is the sample size. n 1 n 1 Gradient: vertical height horizontal distance gradient = vertical height horizontal distance *X * page 0

3 Total marks 45 Attempt ALL questions 1. A baking company will reject cakes if they do not weigh 400 g ± 3%. The weights of a sample of 13 cakes are shown below. 385, 391, 409, 403, 386, 41, 413, 407, 400, 390, 387, 405, 388 Calculate the fraction of cakes that will be rejected. Use your working to justify your answer. 3 *X * page 03 [Turn over

4 . Jennifer is planning to go on a 4 night city break. The costs are shown in the table below. Flights 70 Accommodation 90 per night Spending money 450 Insurance 30 She earns 400 per week. She saves 1 8 of her earnings each week towards her city break. Calculate the minimum number of weeks it will take Jennifer to save enough money for her city break. 3 *X * page 04

5 3. The heights and weights of 8 children aged six are recorded in the table below. Height in centimetres Weight in kilograms (a) On the grid below draw a scattergraph to show this data. (An additional grid, if required, can be found on page 17.) Weight (kilograms) Height (centimetres) (b) Draw a line of best fit on the scattergraph. (c) Use your line of best fit to estimate the height of a child who weighs 0 kilograms. 1 1 *X * page 05 [Turn over

6 4. Lynn is flying an aircraft and has been told that the outside temperature is 34 C lower than the ground temperature. The ground temperature is 6 C. Calculate the outside temperature and mark it on the gauge below. (An additional gauge, if required, can be found on page 18.) C F 140 *X * page 06

7 5. Guests at a wedding were asked to choose their main course. 3 of the guests chose chicken 7 1 of the guests chose beef 3 the remaining guests chose the vegetarian option. Calculate the fraction of guests that chose the vegetarian option Tom thinks that the answer to the following calculation is Is Tom correct? Use your working to justify your answer. *X * page 07 [Turn over

8 7. Gavin is going to South America to do charity work. He changes 750 into Bolivian boliviano. Currency exchange Pounds sterling ( ) Other currencies 1 0 Argentine peso 1 9 Bolivian boliviano 1 4 Brazilian real (a) How many Bolivian boliviano will he receive? 1 He spends 700 Bolivian boliviano. He changes the remaining Bolivian boliviano into Argentine peso. (b) How many Argentine peso will he receive? *X * page 08

9 8. Ian buys a new sofa. The original price was 700. The shop is having a sale with 5% off the price of all sofas. When he goes to the shop he finds there is an additional 5% off the sale price. Calculate the price Ian pays for his sofa. 3 *X * page 09 [Turn over

10 9. Steven flew to Hong Kong to start a new job. The flight included a stop in Doha. He flew from Edinburgh to Doha then from Doha to Hong Kong. The flight from Edinburgh to Doha took 6 hours 35 minutes. The flight from Doha to Hong Kong took 7 hours 0 minutes. Hong Kong is 8 hours ahead of Edinburgh. Steven s plane took off from Edinburgh at 9:15 am local time. It landed in Hong Kong at 8:50 am local time. How long was the stop in Doha? 3 *X * page 10

11 10. David sat a class test. His results are shown in the table below. Marks available Percentage achieved Paper % Paper 65 60% (a) Calculate the number of marks he achieved in paper 1. 1 (b) Calculate his overall percentage for this test 1 *X * page 11 [Turn over

12 11. Ribbon has to be placed around the outside of the love heart cake shown below. 40 cm 34 cm The top of the cake is in the shape of an isosceles triangle with two identical semi-circles. The ribbon needs to be the length of the perimeter of the top of the cake plus an extra 8 cm. Calculate the length of ribbon needed for the cake. Take π = *X * page 1

13 1. A helicopter flew from Aberdeen airport to transport workers to oil rig 1 and then continued on to oil rig. It flew 8 km on a bearing of 04 to oil rig 1. It then flew 46 km on a bearing of 194 to oil rig. (a) Construct a scale drawing to illustrate this journey. Use a scale of 1 cm : 10 km. (An additional diagram, if required, can be found on page 19.) 3 N Airport The helicopter then returns to Aberdeen airport from oil rig. (b) Use the scale drawing to determine the distance and bearing of the airport from oil rig. *X * page 13 [Turn over

14 13. A lawn is to be created in the shape of an isosceles triangle with dimensions as shown below. 10 m 1 m Calculate the area of the lawn. 3 *X * page 14

15 5 14. Michael runs a stall at the school fayre. His game requires two spinners to be spun and allowed to come to rest. The spinners are shown below The numbers on which the spinners come to rest are multiplied together. To win a prize the answer to this multiplication must be less than 5. Calculate the probability of winning a prize. 3 *X * page 15 [Turn over for next question

16 15. A ramp to allow wheelchair access to a school has the dimensions shown below. Height 5 cm ramp Horizontal distance 4 m The maximum gradient allowed for a ramp with a horizontal distance of 1 4 m is 14. Does the gradient of this ramp meet the regulations? Use your working to justify your answer. 3 [END OF QUESTION PAPER] *X * page 16

17 ADDITIONAL SPACE FOR ANSWERS Additional grid for use in question 3 (a) Weight (kilograms) Height (centimetres) *X * page 17

18 ADDITIONAL SPACE FOR ANSWERS Additional gauge for use in question C F 140 *X * page 18

19 ADDITIONAL SPACE FOR ANSWERS Additional diagram for use in question 1 (a) N Airport *X * page 19

20 ADDITIONAL SPACE FOR ANSWERS *X * page 0

21 ADDITIONAL SPACE FOR ANSWERS *X * page 1

22 [BLANK PAGE] WRITE ON PAGE *X * page

23 [BLANK PAGE] WRITE ON PAGE *X * page 3

24 [BLANK PAGE] WRITE ON PAGE *X * page 4

25 N5FOR OFFICIAL USE X844/75/0 National Quali cations 018 Mark Applications of Mathematics Paper THURSDAY, 3 MAY 10:5 AM 1:5 PM *X844750* Fill in these boxes and read what is printed below. Full name of centre Town Forename(s) Surname Number of seat Date of birth Day Month Year Scottish candidate number Total marks 65 Attempt ALL questions. You may use a calculator. To earn full marks you must show your working in your answers. State the units for your answer where appropriate. Write your answers clearly in the spaces provided in this booklet. Additional space for answers is provided at the end of this booklet. If you use this space you must clearly identify the question number you are attempting. Use blue or black ink. Before leaving the examination room you must give this booklet to the Invigilator; if you do not, you may lose all the marks for this paper. *X * A/HTP

26 FORMULAE LIST Circumference of a circle: C = πd Area of a circle: A= πr Theorem of Pythagoras: c b a + b = c a Volume of a cylinder: V= πrh Volume of a prism: V = Ah Volume of a cone: V= 1 πrh 3 Volume of a sphere: V = 4 π 3 3 r Standard deviation: Σ( x x) Σ x (Σ x) n s = =, where n is the sample size. n 1 n 1 Gradient: vertical height horizontal distance gradient = vertical height horizontal distance *X * page 0

27 Total marks 65 Attempt ALL questions 1. Jack bought a car 3 years ago costing The car has decreased in value by 13% each year. (a) Calculate the current value of the car. Give your answer to significant figures. 4 Jack sells his car for 950. (b) Calculate his loss as a percentage of the original price. *X * page 03 [Turn over

28 . The number of podcasts Omar downloaded each month for a year is shown in the table below (a) For this data, calculate: the median the lower quartile the upper quartile. (b) Construct a boxplot for this data. (An additional diagram, if required, can be found on page 1.) *X * page 04

29 3. Ross is changing his internet package. The table below shows the internet packages he is considering. Package Speed (Mbps) Usage Monthly line rental Monthly broadband cost Initial fee Length of contract A 5 5 GB months B 5 Unlimited months C GB or 18 months D 5 Unlimited or 18 months E 5 50 GB for 1st 1 months then Free 4 months Ross requires: a minimum speed of 5 Mbps at least 50 GB of usage a 1 month contract. Ross will choose the package with the lowest overall annual price. Which package will he choose? Use your working to justify your answer. 3 *X * page 05 [Turn over

30 4. Nicola has joined a gym. The pie chart shows the proportion of time that Nicola will spend on each type of workout exercise. Types of workout exercises Warm up Cardiovascular Resistance training Cool down Nicola spent 1 hour and 45 minutes exercising in the gym. (a) Calculate how long, in minutes, Nicola spent on resistance training. Nicola spent 1 minutes exercising on a treadmill. Her average speed was 6 6 km/h. (b) Calculate the distance she ran on the treadmill. *X * page 06

31 5. Three tonnes of sheep food will feed 350 sheep for 18 days. The number of sheep increases by 100. (a) How long will the same weight of food now last? 3 The storage container for the sheep food is in the shape of a cylinder, with dimensions as shown below. 3 8 m 9 7 m (b) Calculate the volume of the storage container. *X * page 07 [Turn over

32 6. Ali, Kate and Jim are paid to deliver leaflets advertising a new restaurant. They shared the money they were paid in a ratio of 3 : 5 : 7. Jim received 154. Calculate how much the restaurant paid, in total, to deliver the leaflets. *X * page 08

33 7. Sam drives from Paris in France to Zurich in Switzerland. He knows: his car will cover an average of 47 miles per gallon of fuel the fuel tank holds 50 litres of fuel when it is full it is 650 km from Paris to Zurich. Will Sam be able to complete his journey with one full tank of fuel? 4 Use your working to justify your answer. 1 mile = km 1 gallon = litres *X * page 09 [Turn over

34 8. Scott decides to build a new track bike. Scott needs to buy a frame, a handlebar, a pair of pedals, a saddle, wheels and tyres. Different retailers offer these parts. The prices, in pounds, are shown in the table. Retailer Handlebar Pedals (pair) Wheels (each) Saddle Tyres (each) Bikes Go Bikevelo Velo cycles Cycle trax EP bikes Scott can buy the parts from different retailers. The bike frame costs (a) Calculate the minimum total cost of the frame and parts. *X * page 10

35 8. (continued) Scott cannot afford to pay for the bike all at once. The cash price of the complete bike from EP bikes is He chooses to buy the complete bike from EP bikes, as they are the only retailer offering a finance package. The finance package consists of: a deposit of 15% of the cash price 36 payments of (b) Calculate how much more this finance package will cost compared to the minimum total cost. 4 *X * page 11 [Turn over

36 8. (continued) Scott trains at the velodrome on his new bike. He records his top speed, in kilometres per hour, for each lap. Six of these speeds are shown below (c) For these speeds, calculate: (i) the mean; 1 (ii) the standard deviation. 3 Scott had a mean top speed on his old bike of 57 3 km/h and a standard deviation of 1 1 km/h. (d) Make two valid comments comparing his top speed on the two different bikes. *X * page 1

37 9. A factory produces cans of tinned beans. The table shows the list of tasks and the time taken to complete them. Task Detail Preceding task Time (seconds) A Boil beans to cook them C 500 B Put on lid H,E 3 C Blanch dried beans in water None 300 D Attach label I 5 E Put sauce in tin F F Make the sauce None 900 G Put in box D 5 H Put beans in tin A I Cook beans in sauce in tin B 300 (a) Complete the diagram below to show the tasks and times in the boxes. (An additional diagram, if required, can be found on page 1.) 1 C 300 The factory manager thinks that the whole process can be completed in less than 5 minutes. (b) Based on the times given, is the factory manager correct? Use your working to justify your answer. *X * page 13 [Turn over

38 9. (continued) The tins are packed in boxes. Each box has dimensions 60 cm 40 cm 15 cm as shown below. 15 cm Store this way up 40 cm 60 cm The boxes must be packed into containers for shipping to Canada. The container has the internal dimensions shown below. 60 cm 40 cm 150 cm All the boxes must be aligned in the same direction. (c) Calculate the maximum number of boxes that will fit in the container. 3 *X * page 14

39 9. (continued) It takes 77 hours to sail from the UK to Canada. The local time in Canada is 5 hours behind the local time in the UK. The ship leaves the UK at 00 on 3rd June. (d) Calculate the date and local time that the ship will arrive in Canada. 3 *X * page 15 [Turn over

40 10. Fiona is a vet. She has started a new job. Her new salary is National Insurance is calculated on a person s salary before deductions such as pension contributions. National Insurance rates Up to % From 8164 to % Over % (a) (i) Calculate Fiona s annual National Insurance payment. Fiona s annual income tax payment is She pays an annual contribution of 3360 into her pension. Fiona is paid in 1 equal monthly payments. (ii) Calculate Fiona s monthly net pay. *X * page 16

41 10. (continued) Fiona plans to rent accommodation. She needs to work out how much she can afford to spend on rent, electricity and council tax. The table shows her monthly outgoings. Outgoings Car payment 395 Car insurance 8 Road tax 1 Food 380 Clothes 130 Mobile phone 64 Internet 55 Socialising 50 Loan 00 Savings 00 Total (b) Calculate how much she will have available per month for rent, electricity and council tax. 1 *X * page 17 [Turn over

42 10. (continued) Fiona is considering these 3 properties. Bedroom House 1 Bedroom Apartment Total Monthly Cost 730 including Rent, Council Tax and Electricity Weekly Rent 13 Council Tax Band F Weekly Electricity 1 3 Bedroom Farmhouse Monthly Rent 390 Council Tax Band E Monthly Electricity 76 Annual Council Tax (to be paid in 1 equal monthly instalments) Band A : Band B : Band C : Band D : Band E : Band F : Band G: 50 4 Band H: (c) Which property is the cheapest option? Use your working to justify your answer. 3 *X * page 18

43 11. A new hotel is being planned in Benidorm. The pool will have a walkway around three sides. The walkway will be 1 5 m wide. This is shown in the diagram. 1 5 m 1 5 m 8 m 1 5 m 16 m (a) Calculate the total area of the walkway. The walkway will be covered in tiles. 16 tiles are needed to cover 1 square metre. The tiles are sold in boxes of 50. Each box costs euro. (b) Calculate the cost of the tiles needed for the walkway. *X * page 19 [Turn over for next question

44 11. (continued) The swimming pool is a prism, with dimensions as shown in the diagram below. 16 m 8 m m 0 5 m 4 m (c) Calculate the volume of the swimming pool. Give your answer in litres. 4 [END OF QUESTION PAPER] *X * page 0

45 ADDITIONAL SPACE FOR ANSWERS Additional diagram for use in question (b) Additional diagram for use in question 9 (a) C 300 *X * page 1

46 ADDITIONAL SPACE FOR ANSWERS *X844750* page

47 ADDITIONAL SPACE FOR ANSWERS *X * page 3

48 ACKNOWLEDGEMENTS Question 9 (c) Evannovostro/Shutterstock.com Question 10 (c) Bedroom House: Ewelina Wachala/Shutterstock.com 1 Bedroom Apartment: Eunika Sopotnicka/Shutterstock.com 3 Bedroom Farmhouse: 1000 Words/Shutterstock.com *X * page 4